This Thesis is concerned with the computation and interpretation of Cerenkov light pulse shapes from digitised pulses. The experiment to measure the characteristics of extensive air showers in the energy range 10(^15) eV - 10(^18) eV was conducted at the University of Durham EAS array in Dugway, UTAH, USA between 1977 and 1980. Systematic environmental monitoring of the experiment has been carried out to quantify weather conditions and assess data quality. Computer programs have been developed and tested to retrieve pulse shape information from digitised Cerenkov light data. Three main data fitting methods are investigated and compared, and the theories underlying them are outlined. A sample of the Dugway data has been analysed in detail after pulse shape reconstruction using unimodal quartic splines. The measured pulse shape parameters are interpreted to show the electron cascade development of the extensive air showers, and related to a proposed primary energy estimator. Suggestions are made for further pulse shape reconstruction techniques.